Problem: Rewrite as a simplified fraction. ${0.71\overline{2} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 712.2222...\\ 100x &= 71.2222...\end{align*}}$ Subtracting the two equations, we have: ${900x = 641}$ ${x = \dfrac{641}{900}} $